Oct 20, 2017 · The maximum number of trees you could build without ending the game is TREE(3). Numerous mathematicians have discovered intriguing things about TREE(3) and this game of trees.

The first significantly large member of the sequence is the famous TREE[3] (also written as TREE(3) [3]), notable because it is a number that appears in serious mathematics that is larger than Graham's number.

Thus TREE(3) > tree $_3$ (tree $_2$ (tree(8))). As you can imagine, the TREE(n) function clearly outpaces the tree(n) function, which is already at the level of the Small Veblen Ordinal in the fast-growing hierarchy.

Oct 11, 2022 · With a little – we stress a little – extra work, we can find that TREE(2) is equal to three. Neither of those are particularly large numbers. So what should we expect TREE(3) to be?

Oct 21, 2017 · What is TREE(3)? It’s a number. An enormous number beyond our ability to express with written notation, beyond what we could even begin to comprehend, bigger than the notoriously gargantuan Graham’s number. We know TREE(3) exists, and we know it’s finite, but we do not know what it is or even how many digits there are.

Jul 16, 2023 · TREE (3) (typically written in all caps) is a classic "unexpectedly large number" in mathematics. The TREE function takes in an integer and spits out an integer. TREE (1) is just 1. TREE (2) is 3. But then TREE (3) is so large that it dwarfs other classic massive numbers like Graham's number.

Apr 7, 2023 · It is physically impossible to contain all the digits of TREE(3) inside your brain – there’s a maximum amount of entropy that can be stored in our heads, and it’s way, way, way less than the ...

Mar 27, 2016 · The really laymen explanation for why TREE(3) is so big goes like this. The TREE(n) function returns the longest possible tree made with N elements that follow very specific rules. These rules guarantee that the resulting longest tree sequence is finite.

TREE(3) or TREE[3] is a massive number made in Kruskal’s TREE Theorem. It’s the first significantly large number in the TREE sequence. It is notoriously very big, and it can’t be easily notated directly.

One can define Z(n) = 0 if TREE(n) finite, undefined otherwise — PA doesn’t prove Z is finite for all n either, yet it is the zero function. Moreover, it should be added that PA does prove that TREE(3) is finite, it just doesn’t prove the statement ‘TREE(n) is finite for all n’.